WASHINGTON — President Barack Obama and leading Republican presidential candidates Mitt Romney and Rick Santorum on Friday said they supported additional investigations into the killing of Trayvon Martin as demonstrations demanding justice for the slain teen continued.

In his first remarks on Martin’s killing, Obama spoke in uncharacteristically personal terms on what he labeled a “tragedy.”

“My main message is to the parents of Trayvon Martin,” Obama said. “You know, if I had a son he’d look like Trayvon, and, you know, I think they are right to expect that all of us, as Americans, are going to take this with the seriousness that it deserves and that we’re going to get to the bottom of exactly what happened.”

Martin’s family thanked the president Friday for bringing attention to their cause.

“The President’s personal comments touched us deeply and made us wonder: If his son looked liked Trayvon and wore a hoodie, would he be suspicious too?” Martin’s family said in a statement.

Martin was shot and killed Feb. 26 near his father’s home in the Orlando suburb of Sanford by volunteer neighborhood watchman George Zimmerman.

Zimmerman, who says he was acting in self-defense when he shot the unarmed teenager, has not been detained or charged in connection with the killing.

The incident ignited a national debate about racism and law enforcement, as well as criticism of Florida’s “Stand Your Ground” law that allows a person to use deadly force when threatened without attempting to retreat.

“There’s a difference between ‘Stand Your Ground’ and doing what [Zimmerman] did and it’s a horrible case,” Rick Santorum said while campaigning in West Monroe, La. “The fact that law enforcement didn’t immediately go after and prosecute this case is another chilling example of you know obviously horrible decisions made by people in this process.”

Mitt Romney also announced his support for investigations into the shooting.

“What happened to Trayvon Martin is a tragedy,” Romney said. “There needs to be a thorough investigation that reassures the public that justice is carried out with impartiality and integrity.”

The politicians’ comments came a day after a flurry of changes in the investigation.

On Thursday, Sanford Police Chief Bill Lee Jr. temporarily stepped down after receiving a vote of no confidence by city commissioners over his department’s handling of the case.

Also Thursday, Florida Attorney General Pam Bondi and Gov. Rick Scott appointed Angela Corey, a Florida State Attorney based in Jacksonville, to replace the local prosecutor in the case. A grand jury is scheduled to convene to probe the shooting on April 10.

Scott additionally announced the creation of a task force to investigate how an incident like Martin’s death could be prevented in the future.

The Justice Department confirmed Thursday that it is conducting an investigation of the incident and said it was still in the fact-gathering stage.

Students staged several mass walk-outs in Miami area schools Friday to demand justice over Martin’s death, and a “Hoodie March” was scheduled to take place in Philadelphia Friday night, among other national demonstrations for Martin.

The Friday protests come on the heels of Al Sharpton’s rally in Sanford Thursday in which the civil rights leader called for Zimmerman’s arrest in front of an audience of nearly 10,000.